Problem: Solve for $x$ and $y$ using substitution. ${5x-5y = 0}$ ${y = -4x+5}$
Explanation: Since $y$ has already been solved for, substitute $-4x+5$ for $y$ in the first equation. ${5x - 5}{(-4x+5)}{= 0}$ Simplify and solve for $x$ $5x+20x - 25 = 0$ $25x-25 = 0$ $25x-25{+25} = 0{+25}$ $25x = 25$ $\dfrac{25x}{{25}} = \dfrac{25}{{25}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {y = -4x+5}\thinspace$ to find $y$ ${y = -4}{(1)}{ + 5}$ $y = -4 + 5$ $y = 1$ You can also plug ${x = 1}$ into $\thinspace {5x-5y = 0}\thinspace$ and get the same answer for $y$ : ${5}{(1)}{ - 5y = 0}$ ${y = 1}$